Second Exam: Thursday 2 April 2015Covers Chapters 5, 8, 9, and 10Lectures 10 to 19 plus Agriculture Global Warming The Vanishing Book of Life on Earth Plastics Intelligent Design?The Weakest Link TechnologyEconomics

Population Growth and Regulation

S - shaped sigmoidal population growth

Verhulst-Pearl Logistic Equation: dN/dt = rN [(K – N)/K]

Assumptions, Derivation

Density Dependence versus Density Independence

Equilibrium, Opportunistic, and Fugitive species

r-selection versus K-selection (r-K selection Continuum)

Correlates of r and K-selection, Bet Hedging

Winemiller’s 3-dimensional fish life history surface

Population Change versus Population Density Plots

Microtine Rodent Population Fluctuations

Hudson Bay Fur Company: Snowshoe Hare and Lynx “Cycles”

http://www.commondreams.org/view/2011/03/07-0

Notice apparent 10-year periodicity

Population “Cycles”• Sunspot Hypothesis• Time Lags• Stress Phenomena Hypothesis• Predator-Prey Oscillations• Epidemiology-Parasite Load Hypothesis• Food Quantity Hypothesis• Nutrient Recovery• Other Food Quality Hypotheses• Genetic Control Hypothesis

Sunspot Hypothesis (Sinclair et al. 1993. Am. Nat.)

10 year cycle embedded within 30-50 year periods

Maunder minimum: 1645-1715

Three periods of high sunspot maxima:

1751-1787 1838-1870 1948-1993

Canadian Government survey 1931-1948

Hare cycle synchronized across North America

Yukon: 5km strip, tree growth rings (N = 368 trees)

One tree germinated in 1675 (>300+ years old)

Hares prefer palatable shrubs,

but will eat spruce

leaving dark tree ring marks

Other Food Quality Hypotheses:

Microtus (Freeland 1974) palatability <–––> toxic

Snowshoe hares: Plant chemical defenses against herbivory

(Bryant 1980)

Chitty’s “Genetic Control” Hypothesis

Could optimal reproductive tactics be involved in driving population cycles?

Population “Cycles”• Sunspot Hypothesis

• Time Lags

• Stress Phenomena Hypothesis

• Predator-Prey Oscillations

• Epidemiology-Parasite Load Hypothesis

• Food Quantity Hypothesis

• Nutrient Recovery

• Other Food Quality Hypotheses

• Genetic Control Hypothesis

Social Behavior

Hermits must have lower fitness than social individualsClumped, random, or dispersed (variance/mean ratio)mobility = motility = vagility (sedentary sessile organisms)

Use of SpacePhilopatryFluid versus Viscous Populations

Individual Distance, Daily MovementsHome RangeTerritoriality (economic defendability)Resource in short supply

Feeding TerritoriesNesting TerritoriesMating Territories

V

V

NetBenefit

Sexual Reproduction

Monoecious versus DieciousEvolution of Sex —> AnisogamyDiploidy as a “fail-safe” mechanismCosts of Sexual Reproduction (halves heritability!)Facultative Sexuality (Ursula LeGuin -- Left Hand of Darkness)Protandry <—> Protogyny (Social control)Parthenogenesis (unisexual species)Possible advantages of sexual reproduction include:

two parents can raise twice as many progeny

mix genes with desirable genes (enhances fitness)reduced sibling competitionheterozygositybiparental origin of many unisexual species

Male

Male

Female

Female = Male Female

No Sex Change Protogyny Protandry

Robert Warner

Why have males? “The biological advantage of a sex ratio that is unbalanced

in favor of females is readily apparent in a species with a

promiscuous mating system. Since one male could fertilize

several females under such a system, survival of a number

of males equal to the number of females would be wasteful

of food, home sites, and other requirements for existence.

The contribution of some of the surplus males to feeding the

predators on the population would be economically

advantageous. In other words, the eating of the less valuable

(to the population) males by predators would tend to

reduce the predator pressure on the more valuable

females.” — Blair (1960) The Rusty Lizard

W. Frank Blair

Sceloporus olivaceus

Sex Ratio

Proportion of MalesPrimary, Secondary, Tertiary, QuaternaryWhy have males?Fisher’s theory: equal investment in the two sexes

Ronald A. Fisher

Comparison of the Contribution to Future Generations of Various Families in Case a in Populations with Different Sex Ratios__________________________________________________________________Case a Number of Males Number of Females__________________________________________________________________Initial population 100 100

Family A 4 0Family C 2 2

Subsequent population (sum) 106 102CA = 4/106 = 0.03773CC = 2/106 + 2/102 = 0.03846 (family C has a higher reproductive success)

__________________________________________________________________

Note: The contribution of family x is designated Cx.

Comparison of the Contribution to Future Generations of Various Families in Case a in Populations with Different Sex Ratios__________________________________________________________________Case a Number of Males Number of Females

__________________________________________________________________

Initial population 100 100Family E 0 4Family C 2 2

Subsequent population (sum) 102 106

CE = 4/106 = 0.03773CC = 2/106 + 2/102 = 0.03846 (family C has a higher reproductive success)

__________________________________________________________________

Note: The contribution of family x is designated Cx.

Comparison of the Contribution to Future Generations of Various Families in Case a in Populations with Different Sex Ratios__________________________________________________________________Case a Number of Males Number of Females

__________________________________________________________________

Initial population 100 100Family A 4 0Family C 2 2Family E 0 4

Subsequent population (sum) 106 106

CA = 4/106 = 0.03773CC = 2/106 + 2/106 = 0.03773 All three families have equal successCE = 4/106 = 0.03773

__________________________________________________________________

Note: The contribution of family x is designated Cx.

___________________________________________________________________________Case b Number of Males Number of Females____________________________________________________________________________Initial population 100 100

Family A 2 0Family B 1 2

Subsequent population (sum) 103 102CA = 2/103 = 0.01942CB = 1/103 + 2/102 = 0.02932 (family B is more successful)

Initial population 100 100Family B 1 2Family C 0 4

Subsequent population (sum) 101 106CB = 1/101 + 2/106 = 0.02877CC = 4/106 = 0.03773 (family C is more successful than family B)

Natural selection will favor families with an excess of females until the population reaches its equilibrium sex ratio (below).Initial population 100 200

Family B 1 2Family C 0 4

Subsequent population (sum) 101 206CB = 1/101 + 2/206 = 0.001971CC = 4/206 = 0.01942 (family B now has the advantage)

_____________________________________________________________________________Note: The contribution of family x is designated Cx.

Differential Mortality of the sexes during the period of parental care.

Differential Mortality of the sexes during the period of parental care